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So
<math display="block"> \frac{\mathrm{d} J_\varepsilon}{\mathrm{d} \varepsilon} = \int_a^b \left[\eta(x) \frac{\partial L_\varepsilon}{\partial g_\varepsilon} + \eta'(x) \frac{\partial L_\varepsilon}{\partial g_\varepsilon'} \, \right]\,\mathrm{d}x \, . </math>
When
<math display="block"> \left.\frac{\mathrm d J_\varepsilon}{\mathrm d\varepsilon}\right|_{\varepsilon=0} = \int_a^b \left[ \eta(x) \frac{\partial L}{\partial f} + \eta'(x) \frac{\partial L}{\partial f'} \,\right]\,\mathrm{d}x = 0 \ .</math>
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